I assume that you are asking how to transfer the activation of a copy of CS3 installed on your home computer to some other system.
The process is very simple. While online (this cannot be done when not connected to the internet), run any one of the CS3 applications and under the "Help" menu bar item, select the "Deactivate" option. That returns an activation associated with your serial number so that you can activate on another system. You don't need to uninstall. You can reverse the process later if necessary. Deactivate on the other system and reactivate when running the app on the home system again. Note that you are limited to 20 such deactivate-activate cycles after which point you may need to contact Adobe Customer Support to restore your ability to do this.
A CS2 serial number has nothing to do with this process.